Transposed Poisson structures on Virasoro-type algebras

TL;DR

This paper classifies all transposed Poisson structures on certain Virasoro-type algebras, providing a detailed analysis of their derivations and algebraic properties.

Contribution

It introduces a comprehensive classification of transposed Poisson structures on deformed and not-finitely graded Heisenberg-Virasoro algebras.

Findings

Computed 1/2-derivations on various Virasoro-type algebras

Classified all transposed Poisson structures on these algebras

Extended understanding of algebraic structures related to Virasoro algebras

Abstract

We compute $\frac{1}{2}$-derivations on the deformed generalized Heisenberg-Virasoro algebras and on not-finitely graded Heisenberg-Virasoro algebras $\widehat{W}_n(G)$, $\widetilde{W}_n(G)$, and $\widetilde{HW}_n(G)$. We classify all transposed Poisson structures on such algebras.